PS 0500: Basic Models of Conflict and Cooperation William Spaniel williamspaniel.com/classes/worldpolitics
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
Under what conditions can two parties play nice with one another?
The Temptation In many circumstances, people have incentive to be mean to one another Example: Your roommate leaves $20 sitting out
The Temptation In many circumstances, people have incentive to be mean to one another Example: Your roommate leaves $20 sitting out Laws make it simple to resist the temptation If you steal the $20, you go to jail
Anarchy, Again No world police exists We cannot just make laws to force two states to be nice to one another Is cooperation impossible under these circumstances? If it is possible, how can we structure interactions to achieve cooperation?
Outline for the Unit How can individually rational behavior lead to collectively bad outcomes?
Outline for the Unit How can individually rational behavior lead to collectively bad outcomes? Can the shadow of future interaction induce two states to play nice with one another?
Outline for the Unit How can individually rational behavior lead to collectively bad outcomes? Can the shadow of future interaction induce two states to play nice with one another? What if the future is never ending?
Outline for the Unit How can individually rational behavior lead to collectively bad outcomes? Can the shadow of future interaction induce two states to play nice with one another? What if the future is never ending? Can two cooperative people nevertheless fail to cooperate?
IR Applications The Cult of the Offensive and the origins of World War I
IR Applications The Cult of the Offensive and the origins of World War I Tariffs and free trade policy
IR Applications The Cult of the Offensive and the origins of World War I Tariffs and free trade policy Arms races and arms treaties
IR Applications The Cult of the Offensive and the origins of World War I Tariffs and free trade policy Arms races and arms treaties The Evolution of Cooperation and trench warfare
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
How can individually rational behavior lead to collectively bad outcomes?
The Situation Two suspects are arrested Police think that they wanted to rob a store But only proof that the suspects were trespassing Thus, police need one of criminals to rat out the other
The Potential Deal If no one confesses to robbery, police can only charge the prisoners for trespassing Punishment: 1 month in jail each If one confesses and the other doesn t, police will be lenient on the rat and severely punish the quiet one: Punishment: 12 months in jail for the quiet one; 0 months for the rat If both confess, police punish both equally Punishment: 8 months in jail each.
The Question No Honor Among Thieves Suppose each thief only wants to minimize the number of months he spends in jail Should they confess to the police?
Neat Result The only reasonable outcome for this game is for both players to confess, even though the <keep quiet, keep quiet> outcome is mutually preferable
Neat Result The only reasonable outcome for this game is for both players to confess, even though the <keep quiet, keep quiet> outcome is mutually preferable Individual incentives explain why
Player 1 s Optimal Strategy Regardless of player 2 s choice, player 1 is better off confessing Therefore, player 1 confesses
Pareto Efficiency The mutual confession outcome is not Pareto efficient Another outcome exists that is better for at least one party without leaving anyone worse off In fact, it leaves both parties better off Major goal in IR: explain why states reach inefficient outcomes
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
Why did World War I start?
The Trivial Explanation Franz Ferdinand was assassinated by Serbian nationalists on June 28, 1914
The Trivial Explanation Franz Ferdinand was assassinated by Serbian nationalists on June 28, 1914 The war started because a dude with a funny mustache died
The Trivial Explanation Franz Ferdinand was assassinated by Serbian nationalists on June 28, 1914 The war started because a dude with a funny mustache died But why are states preemptively declaring war on each other?
The Cult of the Offensive Military and political leaders at the time believed the offense had an enormous advantage New military technology: machine guns, chemical gas, railroads
Strategies and Outcomes Consider a world with two states Two strategies: preempt and defend Ranking the outcomes: 1) I preempt, you defend (Surprise!) 2) We both defend (Peace) 3) We both preempt (War) 4) I defend, you preempt (I m a sucker )
Strategies and Outcomes Consider a world with two states Two strategies: preempt and defend Ranking the outcomes: 1) I preempt, you defend (Surprise!) 2) We both defend (Peace) 3) We both preempt (War) 4) I defend, you preempt (I m a sucker) What have our assumptions bought us?
France s Strategy Regardless of Germany s move, France is always better off preempting Therefore, France preempts
Germany s Strategy Regardless of France s move, Germany is always better off preempting Therefore, Germany preempts This is a prisoner s dilemma Order of the payoffs is identical to before
Conclusion First strike advantages provide a reasonable explanation for the initiation of World War I
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
Why was it so hard to establish free trade?
Fun Fact Free trade is a historically new phenomenon In the past, states set up tariffs (import taxes) on imported goods
Taxes Aren t Fun Tariffs are good for bolstering domestic companies Econ 101: Taxes raise consumer prices, and that s generally a bad thing
The Plight of the Mexican Winery Mexico doesn t have the best grape-producing climate Thus, El Vino Nacional must spend more money to produce quality grapes The company must pass this additional cost onto consumers or go out of business
The Predatory California Winery California has a great climate for grapes and makes wine with ease California companies can flood the Mexican market with wine and put El Vino Nacional out of business But this funnels Mexican money out of Mexico and into California
Solution: Tariffs If Mexico taxes imported wine, prices of Vino Nacional will be competitive Money stays within Mexico
Tequila in California California doesn t have the best agaveproducing climate Californian tequila companies must spend more money to produce quality tequila The company must pass additional cost onto consumers or go out of business
Predatory Mexican Tequila Mexico has a great climate for agave and makes wonderful tequila Mexican companies can flood the Californian market with tequila and put the Californian companies out of business But this funnels American money out of California and into Mexico
Solution: Tariffs If the United States taxes imported tequila, the prices of Californian tequila will be competitive The money stays within California
Outcome Tariffs everywhere! Mexico taxes imports from California California taxes imports from Mexico
Outcome Tariffs everywhere! Mexico taxes imports from California California taxes imports from Mexico Everyone loses (except for the protected businesses)
New Puzzle The prisoner s dilemma predicts that we would see high levels of tariffs This was true before World War II but not the case anymore How have states maintained free trade agreements recently?
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
Why do states engage in arms races?
The Arms Dilemma In a world of anarchy, having military power allows you to get your way
The Arms Dilemma In a world of anarchy, having military power allows you to get your way But military power is relative The Roman Empire was more powerful than Italy is today So a state only makes a relative gain against a rival if it builds and the rival does not
The Arms Dilemma In a world of anarchy, having military power allows you to get your way But military power is relative The Roman Empire was more powerful than Italy is today So a state only makes a relative gain against a rival if it builds and the rival does not Arms are costly to build
New Puzzle The prisoner s dilemma predicts that arms races should be prevalent Yet states sign arms treaties Why are these arms treaties sustainable? Majority of nuclear-capable countries do not have nuclear weapons Why doesn t everyone pull a North Korea?
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
Can future interaction inspire cooperation today?
The Prisoner s Dilemma In a one-shot interaction, the players cannot cooperate because they individually prefer to act aggressively
The Prisoner s Dilemma In a one-shot interaction, the players cannot cooperate because they individually prefer to act aggressively Some interactions are truly one-shot (preemptive war) Others are repetitive (trade, arms races)
The Prisoner s Dilemma In a one-shot interaction, the players cannot cooperate because they individually prefer to act aggressively Some interactions are truly one-shot (preemptive war) Others are repetitive (trade, arms races) Can states cooperate with each other by threatening punishment in the future?
Repeated Play The simplest model: States play the prisoner s dilemma twice Moves from the first round are publicly known in the second round
Repeated Play Can the players cooperate in the first round under threat of punishment in the second round? Is I will cooperate today and, if you cooperate today as well, I will cooperate tomorrow a viable strategy?
Solving the Game Two possible ways to solve: 1. Start by thinking about the first stage and then figure out the second stage 2. Start by thinking about the second stage and then figure out the first stage Which is preferable?
Optimal Strategies Stage 1: Something happens Stage 2: Something already happened, but the states cannot alter their previous payoffs. Therefore, they must optimize their second stage payoffs.
Optimal Strategies Stage 1: Something happens Stage 2: Both players defect
Repeated Play I will cooperate today and, if you cooperate today as well, I will cooperate tomorrow
Optimal Strategies Stage 1: Regardless of what happens in stage 1, the rival will defect in stage 2. Therefore, the states must optimize for today only. Stage 2: Both players defect
Optimal Strategies Stage 1: Both players defect Stage 2: Both players defect
Result Cooperation is not possible with just two interactions Can more interactions help? What if there were n stages?
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1:? Stage n:?
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1:? Stage n: Whatever s happened happened
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1:? Stage n:?
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1:? Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1:? Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1: WHH/future defection certain Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1: Everyone defects Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2:? Stage n 1: Everyone defects Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2: WHH/FDC Stage n 1: Everyone defects Stage n: Everyone defects
Optimal Strategies Stage 1:? Stage 2:? Stage 3:? Stage n 2: Everyone defects Stage n 1: Everyone defects Stage n: Everyone defects
Optimal Strategies Stage 1: Everyone defects Stage 2: Everyone defects Stage 3: Everyone defects Stage n 2: Everyone defects Stage n 1: Everyone defects Stage n: Everyone defects
Outcome Regardless of the length of the interaction, states never cooperate The endgame sabotages cooperation in the earlier stages
New Puzzle What if the shadow of the future is indefinite? We might not know when the interaction will end
Infinite Horizon Model Two states play the prisoner s dilemma repeatedly After every period, they play another period with probability p With probability 1 p, a meteor smashes into the Earth (or something similar) and the game ends
Infinite Horizon Model Two states play the prisoner s dilemma repeatedly After every period, they play another period with probability p With probability 1 p, a meteor smashes into the Earth (or something similar) and the game ends. Also, present values > future values We imagine p to be fairly large
Grim Trigger A tough love strategy Begin by cooperating If at any point in the game a player has defected, defect for the rest of time
Grim Trigger A tough love strategy Begin by cooperating If at any point in the game a player has defected, defect for the rest of time Would two grim trigger players ever have incentive to defect on one another?
Payoffs for Cooperating Forever Today s payoff: 1
Payoffs for Cooperating Forever Today s payoff: 1 Tomorrow s payoff: (p)(1)
Payoffs for Cooperating Forever Today s payoff: 1 Tomorrow s payoff: (p)(1) Day after tomorrow s payoff: (p 2 )(1)
Payoffs for Cooperating Forever Today s payoff: 1 Tomorrow s payoff: (p)(1) Day after tomorrow s payoff: (p 2 )(1) Fourth day s payoff: (p 3 )(1) Fifth day s payoff: (p 4 )(1) Sixth day s payoff: (p 5 )(1) Seventh day s payoff: (p 6 )(1)
Payoffs for Cooperating Forever 1 + (p)(1) + (p 2 )(1) + (p 3 )(1) + (p 4 )(1) + (p 5 )(1) + (p 6 )(1) + (p 7 )(1) + (p 8 )(1) + (p 9 )(1) + (p 10 )(1) + (p 11 )(1) + (p 12 )(1) + (p 13 )(1) + (p 14 )(1) + (p 15 )(1) + (p 16 )(1) + (p 17 )(1) + (p 18 )(1) + (p 19 )(1) + This goes on forever
Payoffs for Cooperating Forever 1 + (p)(1) + (p 2 )(1) + (p 3 )(1) + (p 4 )(1) + (p 5 )(1) + (p 6 )(1) + (p 7 )(1) + (p 8 )(1) + (p 9 )(1) + (p 10 )(1) + (p 11 )(1) + (p 12 )(1) + (p 13 )(1) + (p 14 )(1) + (p 15 )(1) + (p 16 )(1) + (p 17 )(1) + (p 18 )(1) + (p 19 )(1) + This goes on forever Neat math trick: this is finite! Equal to 1/(1 p)
Payoffs for Betrayal If I defect against a grim trigger player, I do slightly better during the first period
Payoffs for Betrayal If I defect against a grim trigger player, I do slightly better during the first period I get 2 instead of 1 However, I do worse for the rest of time
Payoffs for Betrayal If I defect against a grim trigger player, I do slightly better during the first period I get 2 instead of 1 However, I do worse for the rest of time Instead of earning 1 every period, I earn 0 instead The most I can earn from betrayal is 2
Comparing My Choices Payoff for sticking to grim trigger: 1/(1 p) Payoff for betrayal of my opponent: 2
Comparing My Choices Payoff for sticking to grim trigger: 1/(1 p) Payoff for betrayal of my opponent: 2 Therefore, playing cooperatively is in my best interest if: 1/(1 p) 2 1 2(1 p) 1 2 2p p ½
Important Result As long as we are likely to keep interacting in the future, cooperation is possible!
Important Result As long as we are likely to keep interacting in the future, cooperation is possible! Threat of future punishment keeps states in line even without a world police States must not know when the interaction will end ahead of time
Life in WWI Trenches Remember those first strike advantages? Machine guns: good at mowing down oncoming soldiers, bad at overtaking positions Chemical weapons: much harder to use Railroads: great for resupplying troops at the front lines, bad for advancing into enemy territory
Life in WWI Trenches One-shot interaction: they kill each other But trench warfare was different! Sides stayed stationary Enemy troops interacted repeatedly Troops often intentionally shot to miss!
Government Reaction Governments faced compliance problem Incentives of those executing the action were not aligned with those giving the orders Began requiring troops to attempt over the top raids Two possible outcomes Overtake opposing trench Have a lot of dead bodies Verifiable evidence of fighting either way
Robert Axelrod
In Later Lectures Cooperate and defect are very restrictive strategies We need to allow states to bargain with one another
Outline Background The Prisoner s Dilemma The Cult of the Offensive Tariffs and Free Trade Arms Races Repeated Interaction Coordination Problems
What happens if states have nice preferences?
Key Results Players can credibly commit to cooperation in a one-shot game Not possible in a prisoner s dilemma Players have no incentive to follow through on a commitment that says I will cooperate when we play.
Key Results Players can credibly commit to cooperation in a one-shot game Not possible in a prisoner s dilemma Inefficient uncooperative outcome is still possible
Key Results Players can credibly commit to cooperation in a one-shot game Not possible in a prisoner s dilemma Inefficient uncooperative outcome is still possible Stag hunt is a coordination game A primary motivation for international institutions